Question

Find the approximate value of $(9.01{)}^{\frac{1}{2}}$ upto $4$ decimal places.

• A. $3.0001$
• B. $3.0000$
• C. $3.0067$
• D. $3.0017$

Answer 1

The correct option is D $3.0017$

We know that ${(1+x)}^n\approx 1+nx$ when $\left|x\right|<1$

$⟹{\left(9.01\right)}^{\frac{1}{2}}={(9+0.01)}^{\frac{1}{2}}⟹3{(1+\frac{0.01}{9})}^{\frac{1}{2}}\approx 3(1+\frac{0.01}{18})\approx 3.0017$